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Next season's competition is scheduled to begin on September 1 - only a month after the 2020 final - with the showpiece match at Wembley set to take place on May 15, 2021.
"In order to assist in easing pressure on the football schedule, there will be no replays for the 2020-21 season," the FA said in a statement.
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The FA added that the prize fund would return to 2017-18 levels because of the financial impact of the novel coronavirus outbreak after two seasons of record payment levels.
Arsenal beat London rivals Chelsea in the 2020 final on August 1 for a record-extending 14th triumph in the competition.
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